optimization of metal removal rate in turning for aisi...

Columbia International Publishing American Journal of Materials Science & Technology (2015) Vol. 4 No. 2 pp. 93-113 doi:10.7726/ajmst.2015.1008

Research Article

______________________________________________________________________________________________________________________________ *Corresponding e-mail: [email protected] 1 Department of Mechanical Engineering, Khulna University of Engineering and Technology (KUET),

Khulna-9203, Bangladesh

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Optimization of Metal Removal Rate in Turning for AISI 1040 Steel using Taguchi and Fuzzy Logic

Sayed Shafayat Hossain1*, Rubayet Hassan1, and Md. Sajibul Alam Bhuyan1

Received 27 October 2015; Published online 12 December 2015 © The author(s) 2015. Published with open access at www.uscip.us

Abstract Optimization is a system through which superior results are acquired under assured conditions. The challenge of modern manufacturing industries is generally motivated on achieving high quality, high production rate and longer product life with slighter environmental influence. The selection of optimal cutting parameters is a vital concern for all machining processes in order to develop the quality of machining products and diminishes the machining costs. This research work illustrates on the optimization of metal removal rate in turning operation by analyzing the effects of cutting parameters and here Taguchi, ANOVA (Analysis of Variance) & fuzzy logic method are applied to interpret the effect of these parameters on metal removal rate. For investigation, AISI 1040 steel is considered as workpiece where HSS (High Speed Steel) has been used as cutting tool and spindle speed, feed rate & depth of cut have been considered as cutting parameters. The fuzzy optimization that exists in fuzzy modeling enhances this research work more technically sound and sophisticated. Keywords: ANOVA; Design of Experiments; Orthogonal Array; Taguchi Method; Fuzzy logic

1. Introduction Turning is a metal cutting process by which metals from the outer periphery of a cylindrical work piece is removed and the volume of metal removed per unit time is known as metal removal rate or MRR. MRR is a vital criterion in production engineering to increase the productivity and quality. MRR fluctuates with the variation of cutting parameters of different metals. Metal Removal rate has great impact on the mechanical properties such as fatigue, creep, chip formation etc. In the turning operation, vibration is a recurrent and major problem, which shakes the result of the machining and in particular the surface finish. Tool lifespan is also influenced by vibrations. Severe acoustic noise in the working situation normally outcomes as a dynamic motion amid the cutting

Sayed Shafayat Hossain, Rubayet Hassan, and Md. Sajibul Alam Bhuyan / American Journal of Materials Science & Technology (2015) Vol. 4 No. 2 pp. 93-113

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tool and the workpiece. In all cutting operations like turning, boring and milling vibrations are induced due to deformation of the work piece. In the turning process, the significance of machining parameter choice is increased, as it controls the surface quality required and also a crucial factor for productivity.

Fig. 1. Rendered picture of turning operation (Drawn in SolidWorks 2013)

2. Literature Review

Actually an optimization problem is the problem of finding the best solution from all feasible solutions where finding an alternative or parameter with the most cost effective as well as highest achievable performance under the given constraints. Hsu et al. (2006) used multi-objective optimization with a genetic algorithm to investigate the optimal designs of tibial locking screw with respect to bending strength and bone holding power, two important design objectives of locking screws. They created three-dimensional finite element models for analyzing bending strength and bone holding power. After investigation they found the bending strength of tibial locking screws might play a more important role than bone holding power because the loosened screw could still be effective in holding the nail provided it was not completely backed out. Bhattacharjya et al. (2011) showed the application of non-linear mathematical programming technique in the case of optimization problem solving. On this work it has shown that uncertainty is inevitable in the characterization of a structure and disregarding the presence of uncertainty may lead to improper design and catastrophic consequences in many cases. In our research work fuzzy logic has been used to consider the uncertainty and to compare with results derived from ANOVA and Taguchi method. The Taguchi method has been widely used in engineering analysis and is a powerful tool to design a high quality system. Moreover, the Taguchi method employs a special design of orthogonal array to investigate the effects of the entire machining parameters through the small number of experiments. Recently, the Taguchi method has been broadly used in several industrial arenas,


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and research works Lin et al. (2009) and Šibalija et al. (2011). Mariajayaprakash et al. (2013) proved that signal-to-noise (S/N) ratio is used to optimize the shock absorber process parameters. He showd that the Taguchi approach-based thermodynamic model has improved the performance parameters slightly. Washing process parameters (total alkalinity, temperature, pH value of rinsing water, and timing), and painting process parameters (flowability, coating thickness, pointage, and temperature). They used the process parameters, namely, painting and washing process parameters, are optimized by Taguchi method. It was observed that the percentage of defects during the painting process is better than Taguchi method. The predicted range of optimum painting defects is 0.09 < 1.11 < 2.13. Bagci et al. (2006) used the Taguchi method to investigate the influences of drilling parameters on the twist drill bit temperature for a design optimization of cutting parameters. Goharimanesh et al. (2014) worked for improving efficiency in fuel consumption using gearbox optimization using Taguchi quality engineering method, and optimum gear ratios in a five speed gear box is obtained. Analysis of variances disclosed that the significant factor effecting the fuel consumption was gear 5, followed by the differential gear and gear 3. According to the F values, the remaining factors, gear 1, 2 and 4 were not significant. Davim et al. (2003) represented an approach applying the Taguchi method and ANOVA to inaugurate a correlation amid cutting speed and feed rate by the delamination in a composite laminate. A statistical analysis of hole quality was performed by Furness et al. With the expectation of hole location error, the hole quality was not predictably or significantly affected by the cutting conditions. Shivade and Shinde (2014) used wire electrical discharge machining of D3 tool steel for multi-objective optimization in WEDM. Influence of pulse-on time, pulse-off time, peak current and wire speed were investigated for MRR. By Analysis of variance (ANOVA) they showed that the peak current was the most significant parameters affecting on multi-objective characteristics. By taguchi method the ranks and the delta values showed that current had the greatest effect on MRR and was followed by pulse on time, peak current, pulse off time and wire speed in that order. Tsao and Hocheng et al. (2008) performed the extrapolation and estimation of thrust force and exterior roughness in drilling of composite material. They used Taguchi and the artificial neural network methods on this optimization problem. Zhang et al. (2007) performed a study of the Taguchi design application to optimize surface quality in a CNC face milling operation. Taguchi design was successful in optimizing milling parameters for surface roughness. Nalbant et al. (2007) utilized the Taguchi technique to determine the optimal cutting parameters for surface roughness in turning of AISI 1030 steel with TiN coated inserts. Three cutting parameters such as insert radius, feed rate, and depth of cut, are optimized for minimum surface roughness. Kurt et al. (2009) used the Taguchi method in the optimization of cutting parameters for surface finish and hole diameter accuracy in dry drilling processes. Tahriri et al. (2014) studied about the application of fuzzy Delphi and fuzzy inference system in supplier ranking and selection. Here the six aspects and thirteen criteria for supplier selection model were proposed. The six aspects were including trust, quality, cost, delivery, management and organization, financial; in which ‘‘trust’’ and ‘‘cost’’ were ranked as the top two aspects. The second contribution was the development of a multi-criteria decision making model for evaluating the criteria and selecting the appropriate supplier.

3. Methodology 3.1 Specification of Work Material For performing turning operations AISI 1040 steel has been used. They were in the form of


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cylindrical bar of diameter 30mm and cutting length 100mm. The material composition of AISI 1040 steel has given below.

Table 1 Chemical composition of AISI 1040 Steel

C S Mn Fe P

0.37-0.44 0.05 0.6-0.9 Balanced 0.04

3.2 Process parameters

Table 2 Process parameters for investigation.

Level Spindle Speed (s) (rpm) Feed rate(f) (mm/rev) Depth of cut(d) (mm)

1 112 0.125 0.25 2 175 0.138 0.30 3 280 0.153 0.35

3.3 Taguchi Method The Taguchi method has been widely used in engineering investigation and is a powerful contrivance to design a high quality system. Moreover, the Taguchi method employs a special design of orthogonal array to investigate the effects of the entire machining parameters through the small number of experiments (Çiçek et al. 2012). Dr. Genichi Taguchi in 1940s developed a new concept to optimize product/process for engineering experimentation (Singh et al. 2013). The concepts are:

1. Quality should be designed into the product and not inspected into it. 2. Quality is best achieved by minimizing the deviation from the target. It is immune to

uncontrollable environmental factors. 3. The cost of quality should be measured as a function of the deviation from the standard and

the losses should be measured system- wide. 4. It combines the experiment design theory and quadratic quality loss functions have been

applied to the robust design of products and process.

The Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with a small number of experiments (Singh et al. 2013). The change in quality characteristics of a product response to a factor introduced in the experimental design is the signal of the desired effect. The effect of the external factors of the outcome of the quality characteristic under test is termed as noise. To use the loss function as a figure of merit an appropriate loss function with its constant value must first be established which is not always cost effective and easy. The experiment results are then transformed into a Signal-to-Noise (S/N) ratio. Taguchi recommends the use of S/N ratio to measure the quality characteristics deviating from the desired value. The S/N ratio for each level of process parameters is computed based on the S/N analysis and converted into a single metric. The aim in any experiment is to determine the highest possible S/N ratio for the result


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irrespective of the type of the quality characteristics. A high value of S/N implies that signal is much higher than the random effect of noise factors. In the Taguchi method of optimization, the S/N ratio is used as the quality characteristic of choice. The different S/N ratio characteristics are given as (Singh et al. 2013):

I. Nominal-the-Best (NB)/Target-the-Best (TB), II. Lower-the-Better (LB),

III. Higher-the-Better (HB)

3.4 Fuzzy Interference System

Fuzzy logic reflects how people think. It attempts to model our sense of words, our decision making and our common sense. As a result, it is leading to new, more human, intelligent systems.

Fuzzy logic is a set of mathematical principles for knowledge representation based on degrees of membership.

Fuzzy logic is a mathematical theory of inexact reasoning, which allows for the human reasoning process to be modeled in linguistic terms (Lu et al. 2007; Zadeh 1976 & 1994; Mendel et al. 2014; Cox 1992). It is highly suitable for defining the relationship between system input and desired outputs. Fuzzy controllers and fuzzy reasoning have found particular applications in very complex industrial systems which cannot be modeled precisely even under a variety of assumptions and approximations. A fuzzy system is mainly composed of a fuzzifier, an inference engine, a database, a rule base and a defuzzifier. In the study, the fuzzifier first uses membership functions to convert the crisp input into fuzzy sets, and then the inference engine performs a fuzzy reasoning on fuzzy rules to generate fuzzy values. Then, the defuzzifier converts these values into crisp outputs. Fuzzy values are determined by the membership functions, which define the degree of membership of an object in a fuzzy set. However, so far there has been no standard method of choosing the proper shape of the membership functions for the fuzzy set of control variables. Trial and error methods are usually employed. On the basis of fuzzy rules, the Mamdani implication method is employed in this study for fuzzy inference reasoning (Singh et al. 2013).

4. Experimentation and Mathematical Modeling 4.1 Choice of Orthogonal Array Design The choice of a suitable orthogonal array (OA) design is critical for the success of an experiment and depends on the total degrees of freedom required to study the main and interaction effects, the goal of the experiment, resources and budget available and time constraints (Aleksandrovich et al. 2014) Orthogonal arrays allow one to compute the main and interaction effects via a minimum number of experimental trials. ‘‘Degrees of freedom’’ refers to the number of fair and independent comparisons that can be made from a set of observations. In any business finding appropriate method to improve quality and increase productivity plays an important role. The conventional methods based on trial-and-error searches are complex, time-consuming and costly; hence they are changed to the powerful and cost effective statistical methods (Mustafa & Emre 2013). Design of experiment is one of the widely used methods, which is centered on factors, responses, and runs in the experiment process. It is used as an important tool in the engineering design activities and for improving the performance of a manufacturing process. Taguchi’s parameter design is an important


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tool for robust design. Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with a small number of experiments (Maiyar 2013). Taguchi method is one of the important tools used in the industry to shortage product design, develop time and produce lower product cost. This method also takes into consideration the effect of uncontrollable factors on the response. This method is also highly flexible and can allocate different levels of factors, even when the numbers of the levels of factors are not the same (Mustafa & Emre 2013). 4.2 Mathematical Formulation and Experimental Data The experiment is conducted for Dry turning operation (without cutting fluid) of using AISI 1040 mild steel as work material and high speed steel as tool material on a conventional lathe machine. The tests are carried for a 100 mm cutting length of work material. The process parameters used as spindle speed (rpm), feed (mm/rev), depth of cut (mm). The response variable is metal removal rate and the experimental results are recorded in Table 3. Creating orthogonal arrays for the parameter design indicates the number of condition for each experiment. The selection of orthogonal arrays is based on the number of parameters and the level of variation for each parameter. For the maximum metal removal rate, the solution is “Larger is better” and S/N ratio is determined according to the following equation:

S/N = -10 log10 {n-1∑y-2} Where,

S/N = Signal to Noise Ratio, n = No. of Measurements,

y = Measured Value

(a) (b)

Fig. 3. (a) AISI 1040 steel after turning operation (b) High speed steel (HSS) cutting tool.


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Table 3 Experimental data and results for L27 Orthogonal array

Exp no. Spindle speed

(rpm) Feed rate, f (mm/rev)

Depth of cut, d

(mm)

Metal removal rate, MRR

(mm3/s)

1. 112 0.125 0.25 5.56 2. 112 0.125 0.30 6.49 3. 112 0.125 0.35 7.28 4. 112 0.138 0.25 6.23 5. 112 0.138 0.30 7.22 6. 112 0.138 0.35 8.04 7. 112 0.153 0.25 6.43 8. 112 0.153 0.30 7.53 9. 112 0.153 0.35 8.51

10. 175 0.125 0.25 6.71 11. 175 0.125 0.30 7.75 12. 175 0.125 0.35 8.99 13. 175 0.138 0.25 6.58

14. 175 0.138 0.30 7.64

15. 175 0.138 0.35 8.58

16. 175 0.153 0.25 6.79

17. 175 0.153 0.30 7.83

18. 175 0.153 0.35 8.72

19. 280 0.125 0.25 8.16

20. 280 0.125 0.30 9.40

21. 280 0.125 0.35 10.45

22. 280 0.138 0.25 7.72

23. 280 0.138 0.30 8.80

24. 280 0.138 0.35 9.63

25. 280 0.153 0.25 7.80

26. 280 0.153 0.30 8.73

27. 280 0.153 0.35 9.42

Table 4 Response table of means for MRR of AISI 1040 Steel

Level Spindle speed Feed rate Depth of cut

1. 7.03 7.87 6.89

2. 7.73 7.83 7.93

3. 8.90 7.97 8.85


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Table 5 ANOVA for the response Metal removal rate

Source DOF Sum of square Mean of square F ratio % of contribution Spindle speed 2 16.07 8.035 5.74 44.31

Feed rate 2 0.0936 0.0468 0.03 0.26 Depth of cut 2 17.31 8.655 6.18 47.74

Error 2 2.79 1.40 7.69 Total 8 36.26 100

From the above Table 5, it is observed that the spindle speed (44.31%), depth of cut (47.74%) have great influence on metal removal rate. The parameter feed rate (0.26%) has small influence. Since this is a parameter based optimization design, from the above values it is clear that depth of cut (47.74%) is the prime factor to be effectively selected to get the effective metal removal rate. Design of experiment for metal removal rate L9 orthogonal array is prepared by carrying out a total number of 9 experiments along with 2 verification (X and Y data) experiments. For Y data, 9 set of new experiments is conducted in terms of data representation of Table 6. In L9 array 9 rows represent the 9 experiment to be conducted with 3 columns at 3 levels of the corresponding factor. The matrix form of this array is shown in Table 6. Table 6 Calculation of signal to noise ratio for MRR

Exp. No

Parameters level MRR (mm3/s) Signal to noise ratio (S/N ratio)

Spindle speed Feed rate Depth of cut X Y

1. 112 0.125 0.25 5.56 5.60 45.90

2. 112 0.138 0.30 7.22 7.25 50.66

3. 112 0.153 0.35 8.51 8.54 52.08

4. 175 0.125 0.30 7.75 7.78 51.27

5. 175 0.138 0.35 8.58 8.61 51.90

6. 175 0.153 0.25 6.79 6.83 47.63

7. 280 0.125 0.35 10.45 10.50 52.44

8. 280 0.138 0.25 7.72 7.77 46.81

9. 280 0.153 0.30 8.73 8.76 51.24

The experimental data for the metal removal rate values and the calculated signal-to-noise ratio are shown in Table 6. The S/N ratio values of the metal removal rate are calculated, using higher the better characteristics. Conceptual S/N ratio approach of Taguchi method provides a simple, systematic and efficient methodology for optimizing of process parameters and this approach can be adopted rather than using engineering judgment. In practice, the target mean value may change during the process development applications in which the concept of S/N ratio is useful for the improvement of quality through variability reduction and the improvement of measurement. The S/N ratio characteristics can be divided into three categories when the characteristic is continuous: nominal is the best, smaller the better and


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larger is better characteristics. Based on Taguchi prediction that the bigger different in value of S/N ratio shows a more effect on metal removal rate or more significant. Therefore, it can be concluded that, intensification of the depth of cut increases the metal removal rate significantly and it is shown in Table 7. Here delta is the difference between the maximum and minimum value of signal to noise ratio for each parameter. The highest delta value is ranked as first parameter which possesses the maximum influence in metal removal rate of AISI 1040 steel. Table 7 Response table for signal to noise ratio for MRR

level Spindle speed Feed rate Depth of cut 1. 49.54 49.87 46.78 2. 50.27 49.79 51.06 3. 50.17 50.31 52.14

Delta(max-min) 0.73 0.52 5.36 Rank 2 3 1

From Table 7 it is clear that the depth of cut is the most significant parameter for maximizing metal removal rate as its rank is first 4.3 Fuzzy logic model for AISI 1040 in turning operation: (Metal Removal Rate as response)

The modeling of the process has been done using fuzzy interference system (FIS). In this study

three angular membership functions are selected for fuzzy model (fig. 8)

Fig. 8. Fuzzy logic model for AISI 1040 steel in turning operation (response MRR)

A. Membership function for the input and output parameters (MRR as response): This step is to define linguistic values assigned to the variables by the fuzzy subsets and their associated membership functions which may be zero or one called the grades of membership. Zero membership value indicated that it is not a member of the fuzzy set & one represents a complete member. A membership function can have any shape but preferably should be symmetric which includes trapezoidal, triangular & bell shaped. Three membership function were generated for each input variable (Spindle speed, Feed rate, Depth of cut) as shown in fig 9(a, b, c)


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(a)

(b)

(c)

Fig. 9. Membership function plots for input parameters (a) Spindle speed (b) Feed rate (c) Depth of cut

Membership functions for MRR as output variable of the metal is shown in fig. 10

Fig. 10. Membership functions for output parameters (MRR)


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B. FIS rules employed in model (MRR as response): For obtaining optimized solution, the rules at the base have been defined correctly & these rules were written based upon the experimental results. While preparing the rules, fuzzy method was used. Some selected rules are reported in fig.11, fuzzy using MATLAB R2014a using Mamdani type of fuzzy interference system in fuzzy logic toolbox.

Fig. 11. Formulation of rules (Response MRR)


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Fig. 12. Rule viewer of fuzzy model

Fig.12 shows that at spindle speed 112 rpm, feed rate 0.125 mm/rev, depth of cut 0.35mm predicts optimum value of MRR as 3.81 mm3/sec. Similarly, for different sets of data points MRR in turning operation can be predicted from the fuzzy model.


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(a)

(b)

Fig. 13 (a, b). Control surfaces of fuzzy model. Control surfaces in Fig. 13 (a, b) give the interdependency of input & output parameters.


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Table 8 Comparison of fuzzy model and experimental data.

Exp. no. Experimental value of MRR (mm3/sec)

Fuzzy value % variation

1. 5.56 6.14 10.23 2. 6.49 6.00 7.55 3. 7.28 7.02 2.74 4. 6.23 6.14 1.44 5. 7.22 5.93 17.87 6. 8.04 7.87 2.11 7. 6.43 6.14 4.51 8. 7.53 6.03 19.92 9. 8.51 7.87 7.52

10. 6.71 7.89 17.58 11. 7.75 8.44 8.90 12. 8.99 8.41 6.45 13. 6.58 6.14 6.68 14. 7.64 5.98 21.72 15. 8.58 7.87 8.27 16. 6.79 7.89 16.20 17. 7.83 8.22 4.98 18. 8.72 8.15 6.53 19. 8.16 8.49 4.04 20. 9.40 8.50 9.57 21. 10.45 8.49 18.75 22. 7.72 8.49 9.97 23. 8.80 8.50 3.40 24. 9.63 8.49 11.83 25. 7.80 8.49 8.84 26. 8.73 8.49 2.74 27 9.42 8.49 9.87

5. Results and Discussions 5.1 Equation for Optimization of Metal Removal Rate From the linear regression analysis (running a program in Minitab 17) the following equation has derived: MRR= -0.649+0.0111*(Spindle speed) +4.00*(Feed rate) + 19.60*(Depth of cut) 5.2 Graphical Representation From the above experimental results, three methods of data analysis have been used. All methods draw similar conclusions. The depth of cut has found to be the most significant effect to produce


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high value of metal removal rate (MRR). The use of S/N ratio for selecting the best levels of combination for metal removal rate (MRR) value recommends the use of high value of spindle speed & depth of cut in order to obtain good metal removal rate. Therefore, it is preferable to set the depth of cut to a high value. From the table 3 it is clear that the optimal cutting parameters are level 3 of spindle speed & depth of cut and level 1 of feed rate in table 2 to obtain good amount of metal removal rate (MRR) and which is also indicated in table 9. From the result, the interaction of spindle speed and depth of cut is more important than the effect of the individual factors. In other words, in order to get the superlative result it requires experience to combine these two factors to achieve an appropriate combination of spindle speed and depth of cut. Form the graph of the Minitab it is clear that depth of cut has the maximum impact for high metal removal rate. Table 9 Optimal sequence for maximum MRR

Spindle speed Feed rate Depth of cut Metal removal rate (MRR) 280 0.125 0.35 10.45

Fig. 4. Main effects plot for Metal removal rate


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Fig. 5. Interaction plot for Metal removal rate

Fig. 6. Main effects plot for S/N ratio


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Fig. 7. Interaction plot for S/N ratio

(a)

Depth of cut

Sp

ind

le s

pee

d

0.3500.3250.3000.2750.250

280

260

240

220

200

180

160

140

120

>

–

–

–

–

< 6

6 7

7 8

8 9

9 10

10

Rate

Removal

Metal

Contour Plot of Metal Removal Rate vs Spindle speed, Depth of cut


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(b)

Fig. 8 (a, b). Contour plot of (a). MRR Vs. Spindle speed, Depth of cut (b). MRR Vs. Spindle speed, feed rate

6. Conclusion This paper deals with the application of the parameter design (Taguchi method) in the optimization of metal removal rate of AISI 1040 steel in turning operation. ANOVA is required to know the influence of each factors and their quantitative percentage during operation. To acquire the exact percentage of contribution L27 orthogonal array is used in ANOVA analysis whereas for Taguchi method L9 orthogonal array is used. Taguchi method of parameter design can be performed with smaller number of experimentations and for this reason 9 consecutive experiments (L9 in Taguchi’s method) have taken instead of 27 consecutive experiments (L27 in ANOVA). Depth of cut is the most significant parameter which is found for both ANOVA and Taguchi method. The percentage of contribution of the depth of cut parameter is 47.74% in ANOVA analysis and the depth of cut is the first rank in Taguchi method. Taguchi method can be applied for analyzing any other kind of problems as described in this paper. It is found that the parameter design of the Taguchi method offers a simple, logical, and effective approach for optimizing the process parameters and it is one of the most effective techniques in the field of optimization problem solution. Table-8 gives the comparison of the predicted responses using fuzzy model & conducted experimental data. There seems to be a good settlement between fuzzy model & experimental values in all cases. In the present study there are 27 observations & the average percentage error of various responses from fuzzy experimental model has found to be 9.27%. Thus the system has given an overall 90.73%

Feed rate

Sp

ind

le s

peed

0.1500.1450.1400.1350.1300.125

280

260

240

220

200

180

160

140

120

>

–

–

–

–

< 6

6 7

7 8

8 9

9 10

10

Rate

Removal

Metal

Contour Plot of Metal Removal Rate vs Spindle speed, Feed rate


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accuracy from fuzzy model. Since cutting fluid & tool wear investigation is not considered in this research work so there are some variations between experimental & fuzzy values.

Nomenclature s : Spindle speed, rpm. f : Feed rate, mm/rev. d : Depth of cut (DOC), mm. D i : Initial diameter of the metal bar, mm. D f : Final diameter of the metal bar, mm. L : Cutting length of workpiece, mm. t : time, sec. D avg : Average diameter of the cutting section, mm. M.R.R. : Metal removal rate, mm3 /sec. S/N ratio : Signal to noise ratio. X : Metal removal rate for first stage. Y : Metal removal rate for second stage

Acknowledgements We express deep sense of gratitude and indebtedness to Dr. Mohammad Ariful Islam, Professor and Head of the Department of Mechanical Engineering, KUET, Khulna, for his motivation and kind collaboration. We are also grateful to those staff who help us directly or indirectly which was very essential to accelerate our work.

Finally, we are also grateful to the vice chancellor of Khulna University of Engineering and Technology (KUET), Khulna, for his overall support to finish the project works.

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